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All right, so what are we going to do in this exercise, so in this exercise, what we are going to
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do is pretty interesting, OK, not so trivial and not so easy because, you know, like, we are getting
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better and better every exercise and we should also make the exercise a little bit harder.
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So what we are going to do is let me see wrote it down here, so what we are going to do is to make.
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We are going to write right down a recursive function that gets in an integer.
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OK, and these function is going to return one if all the basically the sum of all the numbers in the
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received value is.
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Even OK, otherwise, we should return.
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Return one.
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OK, so a recursive function that gets an integer, let's say, I don't know, some end and an OK in
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these function is going to return one if the sum of all the number of digits.
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OK, I didn't specify if all the sum of all the digits in the received number is even.
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OK, so basically you take all the digits in a given.
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No, you sum them up and you return one if the result is even otherwise, if the result is odd, you
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return zero.
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OK, so a little bit mistake here.
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OK, so that's what you do.
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And basically let's take a look at the example, number one.
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And if the value is, let's say, an equal to one five six, then in this case, if you sum them up,
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that's going to be one plus five, one plus five plus six.
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A total result will be 12.
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And that's an even number and even some because it can be divided by two without the remainder.
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Then that's why the final result, final return value will be in this case one.
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And if the sum.
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OK, let's take another example.
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And if the sum of, I don't know, example to let's say three five.
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OK, something like this.
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Thirty six thousand eight thousand eight hundred fifty nine in this case, the same is going to be like
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three plus six plus eight plus five plus nine, which will leave us a total of what it will give us
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11 plus nine.
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Twenty thirty three, if I'm not mistaken.
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Right.
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So this is nine nine plus nine eighteen plus thirteen.
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The thirty one thirty one Miami stake.
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OK, so thirty one and the final result is going to be zero because the sum is odd.
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OK, so that's what do you have to do in this exercise?
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That's what do you have to practice and to try running this on your own.
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So recursive function.
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Take your time and I'll see you in the Solutions video.
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And of course, by saying the solutions video, I will simply simply think I will make it in this one,
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because you can always pause the video and you can always come back and try writing this code on your
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own.
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So.
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Let us start thinking of what should be the solution, guys.
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OK, so what do you think?
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How should we even start this exercise?
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What do you think?
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What will be the signature of this function?
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What should be its signature?
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So basically, if it's going to return either zero or one, we can always make a boolean result.
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But let's stick with integers just for simplicity, because this section is not about it.
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It's about the recursive manner and the recursive calls.
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So end let's make it, um, I don't know, digits some even.
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OK, and we are going to get value and awesome.
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So now what we have to do is to start thinking of how we can basically even approach this exercise.
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How can we solve it, because that's not so easy and not so trivial is a few examples that we've done
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at the beginning of this section.
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So, guys, what are your thoughts?
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Try to think about it, try to come up with at least one or two options and basically try to run some
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code to see how it works.
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Will it work?
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OK, so think about it.
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Think about it.
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Take some time.
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And once you're done, let's continue to gather.
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OK, so what I suggest to do, first of all, is to think of some logic on how it can be solved.
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So let's just draw something here.
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Let's start with the simple example of one five six.
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OK, so one five six one five six, so what do we want to do is somehow on every on every recursive
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call to check out some status?
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OK, so you have to to think of of some rule that can be applied on every recursive call and basically
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based on these rule, finally, once we will get kind of back from our recursive calls, we will be
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able to make some conclusions for their result so far.
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So if we take one, five, six.
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And we just I don't know, and we just let's think about it together and we just will divide it like
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two, one, five and six, and then we will divide these one five into one and five.
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You know, we'll say the following thing, we'll say that basically we always know we always know that
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the base result will be like probably just one digit because we know that one digit he can be the results
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for it can be decided, you know, like trivially right away.
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So let's start with this with this condition.
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So if and is less than is less than 10, OK, meaning if it's a one digit number, then in this case,
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that's very simple.
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We can say that give and can be divided by two without a remainder, then it means this number is an
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even number that in this case we can return.
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What can we do?
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Return one.
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OK, so if M can be divided by two without the remainder.
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Then we can return one and we can also say the following.
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Let's take like this case, it will be much clearer to you guys.
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So elusive and divided by two does not equal to zero in this case.
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It's an odd number.
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In this way we are going to return zero.
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OK, so if M is less than zero, then we are going to ask if it can be divided by two without a remainder
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returned one otherwise returns zero.
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So that's basically the base case that we can work with.
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Now comes the question of.
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Of what we should we do if it's not the base case?
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OK, so that's the base case, let's say one in five.
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And we know that one in five, for example, for five, we can find the result pretty, pretty easily
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right.
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For or for one.
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We know that one.
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Let's make it like this color.
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And we can say that one is, of course, and definitely one is.
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What is an odd number is an odd number.
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And we are we know that this function is going to return for an odd number.
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It's going to return zero.
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OK, so these function is going to return zero for these base case of one.
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OK, and what I want you to think about is that, first of all, we are probably always going to return
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either one or zero.
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We are not going to return anything else because the final result should be either zero or one.
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And we don't want to like to.
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Mess things up.
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OK, so maybe there is also an option to like to return the some.
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I'm not sure about it, we maybe try to think about it or come up with a solution and let me know in
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the comments and in the questions, if you manage to find another solution to mine by returning this
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sum and finally to making some assumptions and conclusions.
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But for this solution, I'm going to always kind of try to return either a zero or one based on the
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result so far.
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Okay, so now I'm going to say that that's the base case and let's try to try to think about it like.
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The results so far.
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OK, so let's use something like this, let's create additional variable results so far.
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OK, and this variable will have like resolved result result so far is going to be equal to digits,
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some even for.
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I'm just trying to build this together with you.
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OK, so the result is going to be digits, some even for and divided by two, which means without the
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rightmost digit.
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So we know that digits some even can return one.
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If if the sum of all the digits is even otherwise, it will return to zero.
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So we will call the results so far, meaning four one five in this case.
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The results so far, OK, no problem.
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So that's basically how it will look like.
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Let me just draw it here.
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OK, so let's say it's going to be something like this, just trying to draw the structure together
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with you so and equals to one, five, six.
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And then we are going also to call for an equals to one five and also four and equals to six.
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OK, and that's it.
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And on every iteration we are going also to hold a variable.
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This result, let's call it r r equals to this result return from here.
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And this is going to have also the result return from here.
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And basically we know that this equals to six will we will satisfy the base condition.
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It's less than 10.
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And he's going in this case to return one thing since since this value is even.
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OK, so our equals to one.
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And these are equal to one.
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What it indicates is that.
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The results so far result.
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So far.
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Is what is even the result so far, is even.
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OK, OK, so the result so far is even and what can we make out of this conclusion?
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We know that the result so far is even so, we maybe try to kind of formulate a question to see if we
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can like it further.
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It was so oops, my mistake, guys, sorry for that, it's divided every time by 10, so it should be
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like one five in here.
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It should be one.
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I'm sorry.
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Sorry, sorry for that.
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It should be one so and equals to one.
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And here are should be equal to zero since no one is an odd number.
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So that's also I'm going to change here.
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So that's going to be an odd value.
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OK, so results so far is odd.
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OK, so let's try to now proceed.
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And what we are going to do is that we know that we have an equal to one five and we know that the results
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are far from the from the left is an odd result.
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So we are going to ask also a question if.
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What should we ask, what do you think those?
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What do you think we should ask now?
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We can definitely ask about these rightmost digits right now and we can ask if it equals two, basically
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if it's an even or odd.
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So if.
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If.
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How can you find this Redwater statement basically use and do let him write, it will give you the rightmost
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digit in this number and help you find if this result is even or odd, you're basically going to.
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Divided by two, OK, Modula two so if that's the case, if if.
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If it's even then what you are going to do, we're going to ask again.
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Let's ask another question.
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So now if if the results so far results so far, if it was if it was one, it means if the result so
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far is odd, OK, if the result so far is odd, OK, the results so far is odd.
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And these rightmost digit is even then in this case, you know, that is some of odd plus and even will
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always give you a result of OD.
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So that's why you are going to return one.
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And if that's not the case, OK else meaning the result so far equals to zero.
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OK, then it means what it means that the result so far is even OK then in this case you know that we
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are talking about a situation where these digits is even.
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So you know that the result so far is even plus these given digit is even so the final result, the
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sum of them is also going to be even worse.
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And that's why we are going to return zero.
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OK, not so trivial.
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Not so straightforward.
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OK, guys.
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So we took care of the fact when this value is is is even which is not the case here.
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Basically, what we should take care of is also when this and Modula 10, the rightmost digit is in
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the basically I think I've done a little mistake.
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So just with these ones and zeros.
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So if it's an I told you, this exercise is not easy, you should be like very concentrated.
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And now I'm recording this video when I'm not in my fullest concentration.
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So if it's an even, we are going to return once a one relates to even numbers.
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So if it's in, it can be divided by two without a remainder, then it's an even number and the results
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so far equals to one meaning.
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The result is also even three for that then even plus even will result in an even result.
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Otherwise, if the result so far was equal to zero and it was all OK then in this case the sum of odd
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and even will result in odd.
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OK.
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Now, if we have an odd number here, OK, if the number is odd, the rightmost digit is odd and we
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also know that the result so far is even right, because it equals to one that was just in the comments
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and the the the final explanation here, there was this problem, if it's odd and even then the final
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result is zero.
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And otherwise, when the result so far was all the who then the final result of good.
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So let's just remove this one that it won't bother us.
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OK.
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OK, OK, so the results of the result, no problem.
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So we start with this simple question.
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Are digits OK?
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That what we what we want to find digits some even for one, five, six.
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So we want to understand what is this value?
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So we call this function OK.
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We call this function and equals two one five six.
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So the results so far are using these are short R if M is less than zero.
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No, that's not the case.
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So let's find out the results so far.
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Again, the results so far is basically the results so far from the left or the right.
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What do you think?
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Let's proceed.
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So let's proceed.
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Do not answer this question.
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If you are not certain, let's see how we can visualize it.
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So results so far equal two equals two digits, some even for an equals to fifteen.
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OK, so now we come back again here.
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This is another function instance and we ask the following questions.
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We don't know the results of.
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We don't know the results so far again.
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So we called these function four and divided by ten in these just one.
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OK, and here we already know the results so far is going to be returned OK and is less than ten and
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is less than ten.
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The value of end is one that in this case, if M is even that's not it, then we would have been returned
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one otherwise.
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We return zero.
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So from here we return zero.
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And where are the zero is going to be stored in the results of our value in this instance.
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So R equals to zero.
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The result so far is zero, meaning the results so far, ok is what it is.
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It's an odd number.
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OK, so now we come and proceed the running of this instance from this point.
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So if the rightmost element is even, does it even use five and even value the rightmost element so
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anybody will attend the rightmost?
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No, that's not the case.
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So we are going to execute this ls OK.
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And this is going to say the following thing.
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If the result so far was one and it's not meaning it's this ls will be executed.
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The results so far is odd and that's the case are equal to zero then in this case, taking into consideration
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that the result so far is zero, meaning it's in order.
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Right.
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The results so far, the sum of digits so far is odd, plus the current rightmost digit is also odd.
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Then the result should be one because all the plus odd equals two to what do even so, that's why we
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are going to return one to this instance.
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And in this instance we are going to proceed executing these.
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These are from these points.
259
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So R equals to one.
260
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That means we have the sum of digits so far is even.
261
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And we are going to ask if this the rightmost digit is even, does it even?
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Yes, it's six and it's even also even even digit.
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00:21:26,730 --> 00:21:32,790
So we know that even the results of our equals to one meaning, if the results so far is even that's
264
00:21:32,790 --> 00:21:34,620
the case, then returned one.
265
00:21:35,290 --> 00:21:39,990
OK, so even plus even basically will return even.
266
00:21:40,140 --> 00:21:44,580
And that's going to be indicated by the value of one.
267
00:21:46,570 --> 00:21:56,380
Oh, OK, guys, so I think we've managed to kind of solve these difficult exercise together, once
268
00:21:56,380 --> 00:22:03,710
again, we took one, five, six, we split it up to smaller numbers, OK?
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And on every on every iteration, on every basically recursive call, we've compared the sum of digits.
270
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OK, basically, whether it was even even or odd so far, plus the rightmost element for these points.
271
00:22:24,170 --> 00:22:33,820
So we do here are the some so far was one OK, which was an odd number basically indicated by zero and
272
00:22:33,820 --> 00:22:36,610
every time we compare that with the rightmost digit.
273
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So here we compared it with five here we compared it with six because the sum so far was 15.
274
00:22:44,000 --> 00:22:49,720
And we calculated it on this later on this recursive call and so on and so forth.
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So, guys, I'm leaving to you this this example.
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Try to also build these blocks on your own, see what happens.
277
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Make sure that you understand every step and every like every every nuance in this exercise, because
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00:23:08,320 --> 00:23:11,920
these is physically not so trivial.
279
00:23:11,950 --> 00:23:13,290
You have to think about it.
280
00:23:13,300 --> 00:23:16,750
You have to like to try to.
281
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Yeah.
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At least one or two exercises to do like this to make sure you understand everything to the fullest.
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00:23:25,050 --> 00:23:31,590
So with that being said, of course, maybe I will even create additional exercise of just some odd
284
00:23:32,030 --> 00:23:37,800
OK, but there is no much things that should be changed, but I will think about it.
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00:23:38,410 --> 00:23:40,050
So thank you.
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And I will see you next time.
27127
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